The late-stage galaxy merger and prototypical ultraluminous infrared galaxy (ULIRG) Arp 220 is probed using the JWST Mid Infrared Instrument medium-resolution spectrometer to search for multiple diagnostic active galactic nuclei (AGN) emission lines in the low-interstellar-opacity spectral ranges of 5.3–7.9 μm and 12.9–16.0 μm. We detect none of the characteristic high-excitation AGN emission lines. The most diagnostic nondetections are of the [Ne vi] λ 7.652 μm and [Ne v] λ 14.32 μm lines, for which the combined upper limit is ∼10–20 times fainter than the equivalent limit from Spitzer data. We also use X-ray measurements of the reflected Fe Kα line to suggest a relatively low X-ray luminosity. These results suggest that the high obscuration observed along the line of sight to the nuclei of Arp 220 is isotropic and keeps any high-excitation emission from a putative AGN from escaping. An implication is that the observed mid-infrared output of the nuclei is essentially their bolometric luminosity, i.e., no significant additional energy escapes. We utilize this result to show that any embedded AGNs are accreting at no more than ∼5% of the Eddington rate, lower than many theoretical predictions for this stage of ULIRG evolution.